Time evolution of high-energy emissions of low-mass stars : I. Age determination using stellar chronology with white dwarfs in wide binaries

Context. Stellar ages are extremely diffi cult to determine and often subject to large uncertainties, especially for field low-mass stars. We plan to carry out a calibration of the decrease in high-energy emissions of low-mass GKM stars with time, and therefore precise age determination is a key ingredient. The overall goal of our research is to study the time evolution of these high-energy emissions as an essential input to studing exoplanetary atmospheres. Aims. We propose to determine stellar ages with a methodology based on wide binaries. We are interested in systems composed of a low-mass star and a white dwarf (WD), where the latter serves as a stellar chronometer for the system. We aim at obtaining reliable ages for a sample of late-type stars older than 1 Gyr. Methods. We selected a sample of wide binaries composed by a DA type WD and a GKM companion. High signal-to-noise, lowresolution spectroscopic observations were obtained for most of the WD members of the sample. Atmospheric parameters were determined by fitting the spectroscopic data to appropiate W D models. The total ages of the systems were derived by using cooling sequences, an initial-final mass relationship and evolutio nary tracks, to account for the progenitor life. Results. The spectroscopic observations have allowed us to determine ages for the binary systems using WDs as cosmochronometers. We obtained reliable ages for 27 stars between 1 and 5 Gyr, which is a range where age determination becomes diffi cult for field objects. Roughly half of these systems have cooling ages that contribute at least 30% the total age. We select those for fu rther study since their age estimate should be less prone to systematic errors coming from the initial-final mass relationship. Conclusions. We have determined robust ages for a sizeable sample of GKM stars that can be subsequently used to study the time evolution of their emissions associated to stellar magneti c activity.